Plane Light-Like Shells and Impulsive Gravitational Waves in Scalar-Tensor Theories of Gravity

TL;DR

This paper explores exact solutions for impulsive gravitational and electromagnetic waves in scalar-tensor gravity, revealing interactions and singularities, and comparing them to general relativity results.

Contribution

It provides new exact solutions in Brans-Dicke theory describing impulsive waves, null shells, and their interactions, extending understanding beyond general relativity.

Findings

Exact solutions for impulsive gravitational waves in scalar-tensor gravity.

Demonstration of coexistence of gravitational waves and null shells.

Comparison of scalar-tensor solutions with Bell-Szekeres solution in GR.

Abstract

We study gravitational plane impulsive waves and electromagnetic shock waves in a scalar-tensor theory of gravity of the Brans-Dicke type. In vacuum, we present an exact solution of Brans-Dicke's field equations and give an example in which a plane impulsive gravitational wave and a null shell of matter coexist on the same hypersurface. In the homogenous case, we characterize them by their surface energy density and wave amplitude and discuss the inhomogenous case. We also give an exact solution of the Brans-Dicke's field equations in the electrovacuum case which admits a true curvature singularity and use it to built an example where a plane impulsive gravitational wave and an electromagnetic shock wave have the same null hypersurface as history of their wave fronts and propagate independently and decoupled from a null shell of matter. This last solution is shown to correspond to the space-time describing the interaction region resulting from the collision of two electromagnetic shock waves leading to the formation of two gravitational impulsive waves. The properties of this solution are discussed and compared to those of the Bell-Szekeres solution of general relativity.